I don't think that fiat will ever become worthless even price of bitcoin reaches to the moon as everyone is dependent on it for living and even if we have to use bitcoins we need to convert them to fiat first to spend them.
Exactly, yes it will heavily effect the worth of fiat since as most of the people will use bitcoins then the fiat will not be so effective but that been said, fiat has its own value at least till the time when there are almost all the shops which accept bitcoins as payment option.